arXiv:cond-mat/0102425 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Latent heat calculation of the three-dimensional q=3, 4, and 5 Potts models by the tensor product variational approach

Andrej Gendiar, Tomotoshi Nishino

Published Apr 10, 2002• 28 citations

Abstract

Three-dimensional (3D) q-state Potts models (q=3, 4, and 5) are studied by the tensor product variational approach, which is a recently developed variational method for 3D classical lattice models. The variational state is given by a 2D product of local factors, and is improved by way of self-consistent calculations assisted by the corner transfer matrix renormalization group. It should be noted that no a priori condition is imposed for the local factor. Transition temperatures and latent heats are calculated from the observations of thermodynamic functions in both ordered and disordered phases.

DOI: 10.1103/physreve.65.046702

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arXiv:cond-mat/0102425 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Latent heat calculation of the three-dimensional q=3, 4, and 5 Potts models by the tensor product variational approach

Andrej Gendiar, Tomotoshi Nishino

Published Apr 10, 2002• 28 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physreve.65.046702

Related papers

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We propose a numerical self-consistent method for 3D classical lattice models, which optimizes the variational state written as two-dimensional product of tensors. The variational partition function is calculated by the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG). Numerical efficiency of the method is observed via its application to the 3D Ising model. Variational states represented as products of local tensols have been used widely for calculating the ground-state energy in one-dimensional (1D) quantum systems and the free energy in two-dimensional (2D) classical statistical systems. In 1941 Kramers and Wannier calculated a lower bound of the partition function of the 2DWe propose a numerical self-consistent method for 3D classical lattice models, which optimizes the variational state written as two-dimensional product of tensors. The variational partition function is calculated by the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG). Numerical efficiency of the method is observed via its application to the 3D Ising model. Variational states represented as products of local tensols have been used widely for calculating the ground-state energy in one-dimensional (1D) quantum systems and the free energy in two-dimensional (2D) classical statistical systems. In 1941 Kramers and Wannier calculated a lower bound of the partition function of the 2D

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U^{+}

is clearly different from that of the ordered phase

U^{-}

. The obtained latent heat

L = U^{-} - U^{+}

is 0.027, which quantitatively agrees with the exact solution.

β

for the simple 3D Ising model assuming a functional form of the spontaneous magnetization in the off critical region, where the TPVA provides reliable data.